In this paper, dispersion properties and field distributions of surface magneto plasmons (SMPs) in double-layer graphene structures at room temperature are studied. It is found that, the dispersion curves of both symmetric and antisymmetric SMPs modes split into several branches/bands when a magnetic field is applied perpendicularly to the graphene surface. Surprisingly, the lowest energy SMP band has anomalous dependence on the applied magnetic field, different to the other higher bands. In addition, the symmetric and antisymmetric modes can be decoupled if the two graphene layers possess different properties, such as different Fermi energies. Furthermore, electric components of the surface modes which are parallel to the graphene surfaces but perpendicular to the propagation direction (i.e. the transverse-electric mode) are no longer zero caused by the Lorentz force on the free electrons.